Predictive Modeling Applications in Actuarial Science
 Volume 1
 Introduction
 Predictive Modeling Foundations
 Predictive Modeling Methods
 Bayesian and Mixed Modeling
 Longitudinal Modeling
 Volume 2
 Generalized Linear Model
 Extensions of the Generalized Linear Model
 Unsupervised Predictive Modeling Methods

Applications on Current Problems in Actuarial Science
 Chapter 8  The Predictive Distribution of Loss Reserve Estimates over a Finite Time Horizon
 Chapter 9  Finite Mixture Model and Workersâ€™ Compensation LargeLoss Regression Analysis
 Chapter 10  A Framework for Managing Claim Escalation Using Predictive Modeling
 Chapter 11  Predictive Modeling for UsageBased Auto Insurance
Chapter 6  Frequency and Severity Models
Authors
Edward W. Frees  University of WisconsinMadison
jfrees@bus.wisc.edu
Chapter Preview
Many insurance data sets feature information about how often claims arise, the frequency, in addition to the claim size, the severity. This chapter introduces tools for handling the joint distribution of frequency and severity. Frequencyseverity modeling is important in insurance applications because of features of contracts, policyholder behavior, databases that insurers maintain, and regulatory requirements. Model selection depends on the data form. For some data, we observe the claim amount and think about a zero claim as meaning no claim during that period. For other data, we observe individual claim amounts. Model selection also depends upon the purpose of the inference; this chapter highlights the Tweedie generalized linear model as a desirable option. To emphasize practical applications, this chapter features a case study of Massachusetts automobile claims, using outofsample validation for model comparisons.
Data  R Demonstrations  R Code 
Generalized Linear Model: Example  Generalized Linear Model: Example  
Grouped Versus Individual Data Example  Grouped Versus Individual Data Example  
Massachusetts Automobile Example  
Insample Data  Summary Statistics  Summary Statistics 
OutSample Data  Model Fitting  Model Fitting 
OutofSample Validation  OutofSample Validation 